text: /* Rax -- A radix tree implementation.
   *
   * Version 1.2 -- 7 February 2019
   *
   * Copyright (c) 2017-2019, Salvatore Sanfilippo <antirez at gmail dot com>
   * All rights reserved.
   *
   * Redistribution and use in source and binary forms, with or without
   * modification, are permitted provided that the following conditions are met:
   *
   *   * Redistributions of source code must retain the above copyright notice,
   *     this list of conditions and the following disclaimer.
   *   * Redistributions in binary form must reproduce the above copyright
   *     notice, this list of conditions and the following disclaimer in the
   *     documentation and/or other materials provided with the distribution.
   *   * Neither the name of Redis nor the names of its contributors may be used
   *     to endorse or promote products derived from this software without
   *     specific prior written permission.
   *
   * THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS"
   * AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
   * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
   * ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT OWNER OR CONTRIBUTORS BE
   * LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR
   * CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF
   * SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS
   * INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN
   * CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE)
   * ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE
   * POSSIBILITY OF SUCH DAMAGE.
   */
  
  #include <stdlib.h>
  #include <string.h>
  #include <assert.h>
  #include <stdio.h>
  #include <errno.h>
  #include <math.h>
  #include "rax.h"
  
  #ifndef RAX_MALLOC_INCLUDE
  #define RAX_MALLOC_INCLUDE "rax_malloc.h"
  #endif
  
  #include RAX_MALLOC_INCLUDE
  
  /* This is a special pointer that is guaranteed to never have the same value
   * of a radix tree node. It's used in order to report "not found" error without
   * requiring the function to have multiple return values. */
  void *raxNotFound = (void*)"rax-not-found-pointer";
  
  /* -------------------------------- Debugging ------------------------------ */
  
  void raxDebugShowNode(const char *msg, raxNode *n);
  
  /* Turn debugging messages on/off by compiling with RAX_DEBUG_MSG macro on.
   * When RAX_DEBUG_MSG is defined by default Rax operations will emit a lot
   * of debugging info to the standard output, however you can still turn
   * debugging on/off in order to enable it only when you suspect there is an
   * operation causing a bug using the function raxSetDebugMsg(). */
  #ifdef RAX_DEBUG_MSG
  #define debugf(...)                                                            \
      if (raxDebugMsg) {                                                         \
          printf("%s:%s:%d:\t", __FILE__, __func__, __LINE__);                   \
          printf(__VA_ARGS__);                                                   \
          fflush(stdout);                                                        \
      }
  
  #define debugnode(msg,n) raxDebugShowNode(msg,n)
  #else
  #define debugf(...)
  #define debugnode(msg,n)
  #endif
  
  /* By default log debug info if RAX_DEBUG_MSG is defined. */
  static int raxDebugMsg = 1;
  
  /* When debug messages are enabled, turn them on/off dynamically. By
   * default they are enabled. Set the state to 0 to disable, and 1 to
   * re-enable. */
  void raxSetDebugMsg(int onoff) {
      raxDebugMsg = onoff;
  }
  
  /* ------------------------- raxStack functions --------------------------
   * The raxStack is a simple stack of pointers that is capable of switching
   * from using a stack-allocated array to dynamic heap once a given number of
   * items are reached. It is used in order to retain the list of parent nodes
   * while walking the radix tree in order to implement certain operations that
   * need to navigate the tree upward.
   * ------------------------------------------------------------------------- */
  
  /* Initialize the stack. */
  static inline void raxStackInit(raxStack *ts) {
      ts->stack = ts->static_items;
      ts->items = 0;
      ts->maxitems = RAX_STACK_STATIC_ITEMS;
      ts->oom = 0;
  }
  
  /* Push an item into the stack, returns 1 on success, 0 on out of memory. */
  static inline int raxStackPush(raxStack *ts, void *ptr) {
      if (ts->items == ts->maxitems) {
          if (ts->stack == ts->static_items) {
              ts->stack = rax_malloc(sizeof(void*)*ts->maxitems*2);
              if (ts->stack == NULL) {
                  ts->stack = ts->static_items;
                  ts->oom = 1;
                  errno = ENOMEM;
                  return 0;
              }
              memcpy(ts->stack,ts->static_items,sizeof(void*)*ts->maxitems);
          } else {
              void **newalloc = rax_realloc(ts->stack,sizeof(void*)*ts->maxitems*2);
              if (newalloc == NULL) {
                  ts->oom = 1;
                  errno = ENOMEM;
                  return 0;
              }
              ts->stack = newalloc;
          }
          ts->maxitems *= 2;
      }
      ts->stack[ts->items] = ptr;
      ts->items++;
      return 1;
  }
  
  /* Pop an item from the stack, the function returns NULL if there are no
   * items to pop. */
  static inline void *raxStackPop(raxStack *ts) {
      if (ts->items == 0) return NULL;
      ts->items--;
      return ts->stack[ts->items];
  }
  
  /* Return the stack item at the top of the stack without actually consuming
   * it. */
  static inline void *raxStackPeek(raxStack *ts) {
      if (ts->items == 0) return NULL;
      return ts->stack[ts->items-1];
  }
  
  /* Free the stack in case we used heap allocation. */
  static inline void raxStackFree(raxStack *ts) {
      if (ts->stack != ts->static_items) rax_free(ts->stack);
  }
  
  /* ----------------------------------------------------------------------------
   * Radix tree implementation
   * --------------------------------------------------------------------------*/
  
  /* Return the padding needed in the characters section of a node having size
   * 'nodesize'. The padding is needed to store the child pointers to aligned
   * addresses. Note that we add 4 to the node size because the node has a four
   * bytes header. */
  #define raxPadding(nodesize) ((sizeof(void*)-((nodesize+4) % sizeof(void*))) & (sizeof(void*)-1))
  
  /* Return the pointer to the last child pointer in a node. For the compressed
   * nodes this is the only child pointer. */
  #define raxNodeLastChildPtr(n) ((raxNode**) ( \
      ((char*)(n)) + \
      raxNodeCurrentLength(n) - \
      sizeof(raxNode*) - \
      (((n)->iskey && !(n)->isnull) ? sizeof(void*) : 0) \
  ))
  
  /* Return the pointer to the first child pointer. */
  #define raxNodeFirstChildPtr(n) ((raxNode**) ( \
      (n)->data + \
      (n)->size + \
      raxPadding((n)->size)))
  
  /* Return the current total size of the node. Note that the second line
   * computes the padding after the string of characters, needed in order to
   * save pointers to aligned addresses. */
  #define raxNodeCurrentLength(n) ( \
      sizeof(raxNode)+(n)->size+ \
      raxPadding((n)->size)+ \
      ((n)->iscompr ? sizeof(raxNode*) : sizeof(raxNode*)*(n)->size)+ \
      (((n)->iskey && !(n)->isnull)*sizeof(void*)) \
  )
  
  /* Allocate a new non compressed node with the specified number of children.
   * If datafield is true, the allocation is made large enough to hold the
   * associated data pointer.
   * Returns the new node pointer. On out of memory NULL is returned. */
  raxNode *raxNewNode(size_t children, int datafield) {
      size_t nodesize = sizeof(raxNode)+children+raxPadding(children)+
                        sizeof(raxNode*)*children;
      if (datafield) nodesize += sizeof(void*);
      raxNode *node = rax_malloc(nodesize);
      if (node == NULL) return NULL;
      node->iskey = 0;
      node->isnull = 0;
      node->iscompr = 0;
      node->size = children;
      return node;
  }
  
  /* Allocate a new rax and return its pointer. On out of memory the function
   * returns NULL. */
  rax *raxNew(void) {
      rax *rax = rax_malloc(sizeof(*rax));
      if (rax == NULL) return NULL;
      rax->numele = 0;
      rax->numnodes = 1;
      rax->head = raxNewNode(0,0);
      if (rax->head == NULL) {
          rax_free(rax);
          return NULL;
      } else {
          return rax;
      }
  }
  
  /* realloc the node to make room for auxiliary data in order
   * to store an item in that node. On out of memory NULL is returned. */
  raxNode *raxReallocForData(raxNode *n, void *data) {
      if (data == NULL) return n; /* No reallocation needed, setting isnull=1 */
      size_t curlen = raxNodeCurrentLength(n);
      return rax_realloc(n,curlen+sizeof(void*));
  }
  
  /* Set the node auxiliary data to the specified pointer. */
  void raxSetData(raxNode *n, void *data) {
      n->iskey = 1;
      if (data != NULL) {
          n->isnull = 0;
          void **ndata = (void**)
              ((char*)n+raxNodeCurrentLength(n)-sizeof(void*));
          memcpy(ndata,&data,sizeof(data));
      } else {
          n->isnull = 1;
      }
  }
  
  /* Get the node auxiliary data. */
  void *raxGetData(raxNode *n) {
      if (n->isnull) return NULL;
      void **ndata =(void**)((char*)n+raxNodeCurrentLength(n)-sizeof(void*));
      void *data;
      memcpy(&data,ndata,sizeof(data));
      return data;
  }
  
  /* Add a new child to the node 'n' representing the character 'c' and return
   * its new pointer, as well as the child pointer by reference. Additionally
   * '***parentlink' is populated with the raxNode pointer-to-pointer of where
   * the new child was stored, which is useful for the caller to replace the
   * child pointer if it gets reallocated.
   *
   * On success the new parent node pointer is returned (it may change because
   * of the realloc, so the caller should discard 'n' and use the new value).
   * On out of memory NULL is returned, and the old node is still valid. */
  raxNode *raxAddChild(raxNode *n, unsigned char c, raxNode **childptr, raxNode ***parentlink) {
      assert(n->iscompr == 0);
  
      size_t curlen = raxNodeCurrentLength(n);
      n->size++;
      size_t newlen = raxNodeCurrentLength(n);
      n->size--; /* For now restore the original size. We'll update it only on
                    success at the end. */
  
      /* Alloc the new child we will link to 'n'. */
      raxNode *child = raxNewNode(0,0);
      if (child == NULL) return NULL;
  
      /* Make space in the original node. */
      raxNode *newn = rax_realloc(n,newlen);
      if (newn == NULL) {
          rax_free(child);
          return NULL;
      }
      n = newn;
  
      /* After the reallocation, we have up to 8/16 (depending on the system
       * pointer size, and the required node padding) bytes at the end, that is,
       * the additional char in the 'data' section, plus one pointer to the new
       * child, plus the padding needed in order to store addresses into aligned
       * locations.
       *
       * So if we start with the following node, having "abde" edges.
       *
       * Note:
       * - We assume 4 bytes pointer for simplicity.
       * - Each space below corresponds to one byte
       *
       * [HDR*][abde][Aptr][Bptr][Dptr][Eptr]|AUXP|
       *
       * After the reallocation we need: 1 byte for the new edge character
       * plus 4 bytes for a new child pointer (assuming 32 bit machine).
       * However after adding 1 byte to the edge char, the header + the edge
       * characters are no longer aligned, so we also need 3 bytes of padding.
       * In total the reallocation will add 1+4+3 bytes = 8 bytes:
       *
       * (Blank bytes are represented by ".")
       *
       * [HDR*][abde][Aptr][Bptr][Dptr][Eptr]|AUXP|[....][....]
       *
       * Let's find where to insert the new child in order to make sure
       * it is inserted in-place lexicographically. Assuming we are adding
       * a child "c" in our case pos will be = 2 after the end of the following
       * loop. */
      int pos;
      for (pos = 0; pos < n->size; pos++) {
          if (n->data[pos] > c) break;
      }
  
      /* Now, if present, move auxiliary data pointer at the end
       * so that we can mess with the other data without overwriting it.
       * We will obtain something like that:
       *
       * [HDR*][abde][Aptr][Bptr][Dptr][Eptr][....][....]|AUXP|
       */
      unsigned char *src, *dst;
      if (n->iskey && !n->isnull) {
          src = ((unsigned char*)n+curlen-sizeof(void*));
          dst = ((unsigned char*)n+newlen-sizeof(void*));
          memmove(dst,src,sizeof(void*));
      }
  
      /* Compute the "shift", that is, how many bytes we need to move the
       * pointers section forward because of the addition of the new child
       * byte in the string section. Note that if we had no padding, that
       * would be always "1", since we are adding a single byte in the string
       * section of the node (where now there is "abde" basically).
       *
       * However we have padding, so it could be zero, or up to 8.
       *
       * Another way to think at the shift is, how many bytes we need to
       * move child pointers forward *other than* the obvious sizeof(void*)
       * needed for the additional pointer itself. */
      size_t shift = newlen - curlen - sizeof(void*);
  
      /* We said we are adding a node with edge 'c'. The insertion
       * point is between 'b' and 'd', so the 'pos' variable value is
       * the index of the first child pointer that we need to move forward
       * to make space for our new pointer.
       *
       * To start, move all the child pointers after the insertion point
       * of shift+sizeof(pointer) bytes on the right, to obtain:
       *
       * [HDR*][abde][Aptr][Bptr][....][....][Dptr][Eptr]|AUXP|
       */
      src = n->data+n->size+
            raxPadding(n->size)+
            sizeof(raxNode*)*pos;
      memmove(src+shift+sizeof(raxNode*),src,sizeof(raxNode*)*(n->size-pos));
  
      /* Move the pointers to the left of the insertion position as well. Often
       * we don't need to do anything if there was already some padding to use. In
       * that case the final destination of the pointers will be the same, however
       * in our example there was no pre-existing padding, so we added one byte
       * plus there bytes of padding. After the next memmove() things will look
       * like that:
       *
       * [HDR*][abde][....][Aptr][Bptr][....][Dptr][Eptr]|AUXP|
       */
      if (shift) {
          src = (unsigned char*) raxNodeFirstChildPtr(n);
          memmove(src+shift,src,sizeof(raxNode*)*pos);
      }
  
      /* Now make the space for the additional char in the data section,
       * but also move the pointers before the insertion point to the right
       * by shift bytes, in order to obtain the following:
       *
       * [HDR*][ab.d][e...][Aptr][Bptr][....][Dptr][Eptr]|AUXP|
       */
      src = n->data+pos;
      memmove(src+1,src,n->size-pos);
  
      /* We can now set the character and its child node pointer to get:
       *
       * [HDR*][abcd][e...][Aptr][Bptr][....][Dptr][Eptr]|AUXP|
       * [HDR*][abcd][e...][Aptr][Bptr][Cptr][Dptr][Eptr]|AUXP|
       */
      n->data[pos] = c;
      n->size++;
      src = (unsigned char*) raxNodeFirstChildPtr(n);
      raxNode **childfield = (raxNode**)(src+sizeof(raxNode*)*pos);
      memcpy(childfield,&child,sizeof(child));
      *childptr = child;
      *parentlink = childfield;
      return n;
  }
  
  /* Turn the node 'n', that must be a node without any children, into a
   * compressed node representing a set of nodes linked one after the other
   * and having exactly one child each. The node can be a key or not: this
   * property and the associated value if any will be preserved.
   *
   * The function also returns a child node, since the last node of the
   * compressed chain cannot be part of the chain: it has zero children while
   * we can only compress inner nodes with exactly one child each. */
  raxNode *raxCompressNode(raxNode *n, unsigned char *s, size_t len, raxNode **child) {
      assert(n->size == 0 && n->iscompr == 0);
      void *data = NULL; /* Initialized only to avoid warnings. */
      size_t newsize;
  
      debugf("Compress node: %.*s\n", (int)len,s);
  
      /* Allocate the child to link to this node. */
      *child = raxNewNode(0,0);
      if (*child == NULL) return NULL;
  
      /* Make space in the parent node. */
      newsize = sizeof(raxNode)+len+raxPadding(len)+sizeof(raxNode*);
      if (n->iskey) {
          data = raxGetData(n); /* To restore it later. */
          if (!n->isnull) newsize += sizeof(void*);
      }
      raxNode *newn = rax_realloc(n,newsize);
      if (newn == NULL) {
          rax_free(*child);
          return NULL;
      }
      n = newn;
  
      n->iscompr = 1;
      n->size = len;
      memcpy(n->data,s,len);
      if (n->iskey) raxSetData(n,data);
      raxNode **childfield = raxNodeLastChildPtr(n);
      memcpy(childfield,child,sizeof(*child));
      return n;
  }
  
  /* Low level function that walks the tree looking for the string
   * 's' of 'len' bytes. The function returns the number of characters
   * of the key that was possible to process: if the returned integer
   * is the same as 'len', then it means that the node corresponding to the
   * string was found (however it may not be a key in case the node->iskey is
   * zero or if simply we stopped in the middle of a compressed node, so that
   * 'splitpos' is non zero).
   *
   * Otherwise if the returned integer is not the same as 'len', there was an
   * early stop during the tree walk because of a character mismatch.
   *
   * The node where the search ended (because the full string was processed
   * or because there was an early stop) is returned by reference as
   * '*stopnode' if the passed pointer is not NULL. This node link in the
   * parent's node is returned as '*plink' if not NULL. Finally, if the
   * search stopped in a compressed node, '*splitpos' returns the index
   * inside the compressed node where the search ended. This is useful to
   * know where to split the node for insertion.
   *
   * Note that when we stop in the middle of a compressed node with
   * a perfect match, this function will return a length equal to the
   * 'len' argument (all the key matched), and will return a *splitpos which is
   * always positive (that will represent the index of the character immediately
   * *after* the last match in the current compressed node).
   *
   * When instead we stop at a compressed node and *splitpos is zero, it
   * means that the current node represents the key (that is, none of the
   * compressed node characters are needed to represent the key, just all
   * its parents nodes). */
  static inline size_t raxLowWalk(rax *rax, unsigned char *s, size_t len, raxNode **stopnode, raxNode ***plink, int *splitpos, raxStack *ts) {
      raxNode *h = rax->head;
      raxNode **parentlink = &rax->head;
  
      size_t i = 0; /* Position in the string. */
      size_t j = 0; /* Position in the node children (or bytes if compressed).*/
      while(h->size && i < len) {
          debugnode("Lookup current node",h);
          unsigned char *v = h->data;
  
          if (h->iscompr) {
              for (j = 0; j < h->size && i < len; j++, i++) {
                  if (v[j] != s[i]) break;
              }
              if (j != h->size) break;
          } else {
              /* Even when h->size is large, linear scan provides good
               * performances compared to other approaches that are in theory
               * more sounding, like performing a binary search. */
              for (j = 0; j < h->size; j++) {
                  if (v[j] == s[i]) break;
              }
              if (j == h->size) break;
              i++;
          }
  
          if (ts) raxStackPush(ts,h); /* Save stack of parent nodes. */
          raxNode **children = raxNodeFirstChildPtr(h);
          if (h->iscompr) j = 0; /* Compressed node only child is at index 0. */
          memcpy(&h,children+j,sizeof(h));
          parentlink = children+j;
          j = 0; /* If the new node is non compressed and we do not
                    iterate again (since i == len) set the split
                    position to 0 to signal this node represents
                    the searched key. */
      }
      debugnode("Lookup stop node is",h);
      if (stopnode) *stopnode = h;
      if (plink) *plink = parentlink;
      if (splitpos && h->iscompr) *splitpos = j;
      return i;
  }
  
  /* Insert the element 's' of size 'len', setting as auxiliary data
   * the pointer 'data'. If the element is already present, the associated
   * data is updated (only if 'overwrite' is set to 1), and 0 is returned,
   * otherwise the element is inserted and 1 is returned. On out of memory the
   * function returns 0 as well but sets errno to ENOMEM, otherwise errno will
   * be set to 0.
   */
  int raxGenericInsert(rax *rax, unsigned char *s, size_t len, void *data, void **old, int overwrite) {
      size_t i;
      int j = 0; /* Split position. If raxLowWalk() stops in a compressed
                    node, the index 'j' represents the char we stopped within the
                    compressed node, that is, the position where to split the
                    node for insertion. */
      raxNode *h, **parentlink;
  
      debugf("### Insert %.*s with value %p\n", (int)len, s, data);
      i = raxLowWalk(rax,s,len,&h,&parentlink,&j,NULL);
  
      /* If i == len we walked following the whole string. If we are not
       * in the middle of a compressed node, the string is either already
       * inserted or this middle node is currently not a key, but can represent
       * our key. We have just to reallocate the node and make space for the
       * data pointer. */
      if (i == len && (!h->iscompr || j == 0 /* not in the middle if j is 0 */)) {
          debugf("### Insert: node representing key exists\n");
          /* Make space for the value pointer if needed. */
          if (!h->iskey || (h->isnull && overwrite)) {
              h = raxReallocForData(h,data);
              if (h) memcpy(parentlink,&h,sizeof(h));
          }
          if (h == NULL) {
              errno = ENOMEM;
              return 0;
          }
  
          /* Update the existing key if there is already one. */
          if (h->iskey) {
              if (old) *old = raxGetData(h);
              if (overwrite) raxSetData(h,data);
              errno = 0;
              return 0; /* Element already exists. */
          }
  
          /* Otherwise set the node as a key. Note that raxSetData()
           * will set h->iskey. */
          raxSetData(h,data);
          rax->numele++;
          return 1; /* Element inserted. */
      }
  
      /* If the node we stopped at is a compressed node, we need to
       * split it before to continue.
       *
       * Splitting a compressed node have a few possible cases.
       * Imagine that the node 'h' we are currently at is a compressed
       * node containing the string "ANNIBALE" (it means that it represents
       * nodes A -> N -> N -> I -> B -> A -> L -> E with the only child
       * pointer of this node pointing at the 'E' node, because remember that
       * we have characters at the edges of the graph, not inside the nodes
       * themselves.
       *
       * In order to show a real case imagine our node to also point to
       * another compressed node, that finally points at the node without
       * children, representing 'O':
       *
       *     "ANNIBALE" -> "SCO" -> []
       *
       * When inserting we may face the following cases. Note that all the cases
       * require the insertion of a non compressed node with exactly two
       * children, except for the last case which just requires splitting a
       * compressed node.
       *
       * 1) Inserting "ANNIENTARE"
       *
       *               |B| -> "ALE" -> "SCO" -> []
       *     "ANNI" -> |-|
       *               |E| -> (... continue algo ...) "NTARE" -> []
       *
       * 2) Inserting "ANNIBALI"
       *
       *                  |E| -> "SCO" -> []
       *     "ANNIBAL" -> |-|
       *                  |I| -> (... continue algo ...) []
       *
       * 3) Inserting "AGO" (Like case 1, but set iscompr = 0 into original node)
       *
       *            |N| -> "NIBALE" -> "SCO" -> []
       *     |A| -> |-|
       *            |G| -> (... continue algo ...) |O| -> []
       *
       * 4) Inserting "CIAO"
       *
       *     |A| -> "NNIBALE" -> "SCO" -> []
       *     |-|
       *     |C| -> (... continue algo ...) "IAO" -> []
       *
       * 5) Inserting "ANNI"
       *
       *     "ANNI" -> "BALE" -> "SCO" -> []
       *
       * The final algorithm for insertion covering all the above cases is as
       * follows.
       *
       * ============================= ALGO 1 =============================
       *
       * For the above cases 1 to 4, that is, all cases where we stopped in
       * the middle of a compressed node for a character mismatch, do:
       *
       * Let $SPLITPOS be the zero-based index at which, in the
       * compressed node array of characters, we found the mismatching
       * character. For example if the node contains "ANNIBALE" and we add
       * "ANNIENTARE" the $SPLITPOS is 4, that is, the index at which the
       * mismatching character is found.
       *
       * 1. Save the current compressed node $NEXT pointer (the pointer to the
       *    child element, that is always present in compressed nodes).
       *
       * 2. Create "split node" having as child the non common letter
       *    at the compressed node. The other non common letter (at the key)
       *    will be added later as we continue the normal insertion algorithm
       *    at step "6".
       *
       * 3a. IF $SPLITPOS == 0:
       *     Replace the old node with the split node, by copying the auxiliary
       *     data if any. Fix parent's reference. Free old node eventually
       *     (we still need its data for the next steps of the algorithm).
       *
       * 3b. IF $SPLITPOS != 0:
       *     Trim the compressed node (reallocating it as well) in order to
       *     contain $splitpos characters. Change child pointer in order to link
       *     to the split node. If new compressed node len is just 1, set
       *     iscompr to 0 (layout is the same). Fix parent's reference.
       *
       * 4a. IF the postfix len (the length of the remaining string of the
       *     original compressed node after the split character) is non zero,
       *     create a "postfix node". If the postfix node has just one character
       *     set iscompr to 0, otherwise iscompr to 1. Set the postfix node
       *     child pointer to $NEXT.
       *
       * 4b. IF the postfix len is zero, just use $NEXT as postfix pointer.
       *
       * 5. Set child[0] of split node to postfix node.
       *
       * 6. Set the split node as the current node, set current index at child[1]
       *    and continue insertion algorithm as usually.
       *
       * ============================= ALGO 2 =============================
       *
       * For case 5, that is, if we stopped in the middle of a compressed
       * node but no mismatch was found, do:
       *
       * Let $SPLITPOS be the zero-based index at which, in the
       * compressed node array of characters, we stopped iterating because
       * there were no more keys character to match. So in the example of
       * the node "ANNIBALE", adding the string "ANNI", the $SPLITPOS is 4.
       *
       * 1. Save the current compressed node $NEXT pointer (the pointer to the
       *    child element, that is always present in compressed nodes).
       *
       * 2. Create a "postfix node" containing all the characters from $SPLITPOS
       *    to the end. Use $NEXT as the postfix node child pointer.
       *    If the postfix node length is 1, set iscompr to 0.
       *    Set the node as a key with the associated value of the new
       *    inserted key.
       *
       * 3. Trim the current node to contain the first $SPLITPOS characters.
       *    As usually if the new node length is just 1, set iscompr to 0.
       *    Take the iskey / associated value as it was in the original node.
       *    Fix the parent's reference.
       *
       * 4. Set the postfix node as the only child pointer of the trimmed
       *    node created at step 1.
       */
  
      /* ------------------------- ALGORITHM 1 --------------------------- */
      if (h->iscompr && i != len) {
          debugf("ALGO 1: Stopped at compressed node %.*s (%p)\n",
              h->size, h->data, (void*)h);
          debugf("Still to insert: %.*s\n", (int)(len-i), s+i);
          debugf("Splitting at %d: '%c'\n", j, ((char*)h->data)[j]);
          debugf("Other (key) letter is '%c'\n", s[i]);
  
          /* 1: Save next pointer. */
          raxNode **childfield = raxNodeLastChildPtr(h);
          raxNode *next;
          memcpy(&next,childfield,sizeof(next));
          debugf("Next is %p\n", (void*)next);
          debugf("iskey %d\n", h->iskey);
          if (h->iskey) {
              debugf("key value is %p\n", raxGetData(h));
          }
  
          /* Set the length of the additional nodes we will need. */
          size_t trimmedlen = j;
          size_t postfixlen = h->size - j - 1;
          int split_node_is_key = !trimmedlen && h->iskey && !h->isnull;
          size_t nodesize;
  
          /* 2: Create the split node. Also allocate the other nodes we'll need
           *    ASAP, so that it will be simpler to handle OOM. */
          raxNode *splitnode = raxNewNode(1, split_node_is_key);
          raxNode *trimmed = NULL;
          raxNode *postfix = NULL;
  
          if (trimmedlen) {
              nodesize = sizeof(raxNode)+trimmedlen+raxPadding(trimmedlen)+
                         sizeof(raxNode*);
              if (h->iskey && !h->isnull) nodesize += sizeof(void*);
              trimmed = rax_malloc(nodesize);
          }
  
          if (postfixlen) {
              nodesize = sizeof(raxNode)+postfixlen+raxPadding(postfixlen)+
                         sizeof(raxNode*);
              postfix = rax_malloc(nodesize);
          }
  
          /* OOM? Abort now that the tree is untouched. */
          if (splitnode == NULL ||
              (trimmedlen && trimmed == NULL) ||
              (postfixlen && postfix == NULL))
          {
              rax_free(splitnode);
              rax_free(trimmed);
              rax_free(postfix);
              errno = ENOMEM;
              return 0;
          }
          splitnode->data[0] = h->data[j];
  
          if (j == 0) {
              /* 3a: Replace the old node with the split node. */
              if (h->iskey) {
                  void *ndata = raxGetData(h);
                  raxSetData(splitnode,ndata);
              }
              memcpy(parentlink,&splitnode,sizeof(splitnode));
          } else {
              /* 3b: Trim the compressed node. */
              trimmed->size = j;
              memcpy(trimmed->data,h->data,j);
              trimmed->iscompr = j > 1 ? 1 : 0;
              trimmed->iskey = h->iskey;
              trimmed->isnull = h->isnull;
              if (h->iskey && !h->isnull) {
                  void *ndata = raxGetData(h);
                  raxSetData(trimmed,ndata);
              }
              raxNode **cp = raxNodeLastChildPtr(trimmed);
              memcpy(cp,&splitnode,sizeof(splitnode));
              memcpy(parentlink,&trimmed,sizeof(trimmed));
              parentlink = cp; /* Set parentlink to splitnode parent. */
              rax->numnodes++;
          }
  
          /* 4: Create the postfix node: what remains of the original
           * compressed node after the split. */
          if (postfixlen) {
              /* 4a: create a postfix node. */
              postfix->iskey = 0;
              postfix->isnull = 0;
              postfix->size = postfixlen;
              postfix->iscompr = postfixlen > 1;
              memcpy(postfix->data,h->data+j+1,postfixlen);
              raxNode **cp = raxNodeLastChildPtr(postfix);
              memcpy(cp,&next,sizeof(next));
              rax->numnodes++;
          } else {
              /* 4b: just use next as postfix node. */
              postfix = next;
          }
  
          /* 5: Set splitnode first child as the postfix node. */
          raxNode **splitchild = raxNodeLastChildPtr(splitnode);
          memcpy(splitchild,&postfix,sizeof(postfix));
  
          /* 6. Continue insertion: this will cause the splitnode to
           * get a new child (the non common character at the currently
           * inserted key). */
          rax_free(h);
          h = splitnode;
      } else if (h->iscompr && i == len) {
      /* ------------------------- ALGORITHM 2 --------------------------- */
          debugf("ALGO 2: Stopped at compressed node %.*s (%p) j = %d\n",
              h->size, h->data, (void*)h, j);
  
          /* Allocate postfix & trimmed nodes ASAP to fail for OOM gracefully. */
          size_t postfixlen = h->size - j;
          size_t nodesize = sizeof(raxNode)+postfixlen+raxPadding(postfixlen)+
                            sizeof(raxNode*);
          if (data != NULL) nodesize += sizeof(void*);
          raxNode *postfix = rax_malloc(nodesize);
  
          nodesize = sizeof(raxNode)+j+raxPadding(j)+sizeof(raxNode*);
          if (h->iskey && !h->isnull) nodesize += sizeof(void*);
          raxNode *trimmed = rax_malloc(nodesize);
  
          if (postfix == NULL || trimmed == NULL) {
              rax_free(postfix);
              rax_free(trimmed);
              errno = ENOMEM;
              return 0;
          }
  
          /* 1: Save next pointer. */
          raxNode **childfield = raxNodeLastChildPtr(h);
          raxNode *next;
          memcpy(&next,childfield,sizeof(next));
  
          /* 2: Create the postfix node. */
          postfix->size = postfixlen;
          postfix->iscompr = postfixlen > 1;
          postfix->iskey = 1;
          postfix->isnull = 0;
          memcpy(postfix->data,h->data+j,postfixlen);
          raxSetData(postfix,data);
          raxNode **cp = raxNodeLastChildPtr(postfix);
          memcpy(cp,&next,sizeof(next));
          rax->numnodes++;
  
          /* 3: Trim the compressed node. */
          trimmed->size = j;
          trimmed->iscompr = j > 1;
          trimmed->iskey = 0;
          trimmed->isnull = 0;
          memcpy(trimmed->data,h->data,j);
          memcpy(parentlink,&trimmed,sizeof(trimmed));
          if (h->iskey) {
              void *aux = raxGetData(h);
              raxSetData(trimmed,aux);
          }
  
          /* Fix the trimmed node child pointer to point to
           * the postfix node. */
          cp = raxNodeLastChildPtr(trimmed);
          memcpy(cp,&postfix,sizeof(postfix));
  
          /* Finish! We don't need to continue with the insertion
           * algorithm for ALGO 2. The key is already inserted. */
          rax->numele++;
          rax_free(h);
          return 1; /* Key inserted. */
      }
  
      /* We walked the radix tree as far as we could, but still there are left
       * chars in our string. We need to insert the missing nodes. */
      while(i < len) {
          raxNode *child;
  
          /* If this node is going to have a single child, and there
           * are other characters, so that that would result in a chain
           * of single-childed nodes, turn it into a compressed node. */
          if (h->size == 0 && len-i > 1) {
              debugf("Inserting compressed node\n");
              size_t comprsize = len-i;
              if (comprsize > RAX_NODE_MAX_SIZE)
                  comprsize = RAX_NODE_MAX_SIZE;
              raxNode *newh = raxCompressNode(h,s+i,comprsize,&child);
              if (newh == NULL) goto oom;
              h = newh;
              memcpy(parentlink,&h,sizeof(h));
              parentlink = raxNodeLastChildPtr(h);
              i += comprsize;
          } else {
              debugf("Inserting normal node\n");
              raxNode **new_parentlink;
              raxNode *newh = raxAddChild(h,s[i],&child,&new_parentlink);
              if (newh == NULL) goto oom;
              h = newh;
              memcpy(parentlink,&h,sizeof(h));
              parentlink = new_parentlink;
              i++;
          }
          rax->numnodes++;
          h = child;
      }
      raxNode *newh = raxReallocForData(h,data);
      if (newh == NULL) goto oom;
      h = newh;
      if (!h->iskey) rax->numele++;
      raxSetData(h,data);
      memcpy(parentlink,&h,sizeof(h));
      return 1; /* Element inserted. */
  
  oom:
      /* This code path handles out of memory after part of the sub-tree was
       * already modified. Set the node as a key, and then remove it. However we
       * do that only if the node is a terminal node, otherwise if the OOM
       * happened reallocating a node in the middle, we don't need to free
       * anything. */
      if (h->size == 0) {
          h->isnull = 1;
          h->iskey = 1;
          rax->numele++; /* Compensate the next remove. */
          assert(raxRemove(rax,s,i,NULL) != 0);
      }
      errno = ENOMEM;
      return 0;
  }
  
  /* Overwriting insert. Just a wrapper for raxGenericInsert() that will
   * update the element if there is already one for the same key. */
  int raxInsert(rax *rax, unsigned char *s, size_t len, void *data, void **old) {
      return raxGenericInsert(rax,s,len,data,old,1);
  }
  
  /* Non overwriting insert function: this if an element with the same key
   * exists, the value is not updated and the function returns 0.
   * This is a just a wrapper for raxGenericInsert(). */
  int raxTryInsert(rax *rax, unsigned char *s, size_t len, void *data, void **old) {
      return raxGenericInsert(rax,s,len,data,old,0);
  }
  
  /* Find a key in the rax, returns raxNotFound special void pointer value
   * if the item was not found, otherwise the value associated with the
   * item is returned. */
  void *raxFind(rax *rax, unsigned char *s, size_t len) {
      raxNode *h;
  
      debugf("### Lookup: %.*s\n", (int)len, s);
      int splitpos = 0;
      size_t i = raxLowWalk(rax,s,len,&h,NULL,&splitpos,NULL);
      if (i != len || (h->iscompr && splitpos != 0) || !h->iskey)
          return raxNotFound;
      return raxGetData(h);
  }
  
  /* Return the memory address where the 'parent' node stores the specified
   * 'child' pointer, so that the caller can update the pointer with another
   * one if needed. The function assumes it will find a match, otherwise the
   * operation is an undefined behavior (it will continue scanning the
   * memory without any bound checking). */
  raxNode **raxFindParentLink(raxNode *parent, raxNode *child) {
      raxNode **cp = raxNodeFirstChildPtr(parent);
      raxNode *c;
      while(1) {
          memcpy(&c,cp,sizeof(c));
          if (c == child) break;
          cp++;
      }
      return cp;
  }
  
  /* Low level child removal from node. The new node pointer (after the child
   * removal) is returned. Note that this function does not fix the pointer
   * of the parent node in its parent, so this task is up to the caller.
   * The function never fails for out of memory. */
  raxNode *raxRemoveChild(raxNode *parent, raxNode *child) {
      debugnode("raxRemoveChild before", parent);
      /* If parent is a compressed node (having a single child, as for definition
       * of the data structure), the removal of the child consists into turning
       * it into a normal node without children. */
      if (parent->iscompr) {
          void *data = NULL;
          if (parent->iskey) data = raxGetData(parent);
          parent->isnull = 0;
          parent->iscompr = 0;
          parent->size = 0;
          if (parent->iskey) raxSetData(parent,data);
          debugnode("raxRemoveChild after", parent);
          return parent;
      }
  
      /* Otherwise we need to scan for the child pointer and memmove()
       * accordingly.
       *
       * 1. To start we seek the first element in both the children
       *    pointers and edge bytes in the node. */
      raxNode **cp = raxNodeFirstChildPtr(parent);
      raxNode **c = cp;
      unsigned char *e = parent->data;
  
      /* 2. Search the child pointer to remove inside the array of children
       *    pointers. */
      while(1) {
          raxNode *aux;
          memcpy(&aux,c,sizeof(aux));
          if (aux == child) break;
          c++;
          e++;
      }
  
      /* 3. Remove the edge and the pointer by memmoving the remaining children
       *    pointer and edge bytes one position before. */
      int taillen = parent->size - (e - parent->data) - 1;
      debugf("raxRemoveChild tail len: %d\n", taillen);
      memmove(e,e+1,taillen);
  
      /* Compute the shift, that is the amount of bytes we should move our
       * child pointers to the left, since the removal of one edge character
       * and the corresponding padding change, may change the layout.
       * We just check if in the old version of the node there was at the
       * end just a single byte and all padding: in that case removing one char
       * will remove a whole sizeof(void*) word. */
      size_t shift = ((parent->size+4) % sizeof(void*)) == 1 ? sizeof(void*) : 0;
  
      /* Move the children pointers before the deletion point. */
      if (shift)
          memmove(((char*)cp)-shift,cp,(parent->size-taillen-1)*sizeof(raxNode**));
  
      /* Move the remaining "tail" pointers at the right position as well. */
      size_t valuelen = (parent->iskey && !parent->isnull) ? sizeof(void*) : 0;
      memmove(((char*)c)-shift,c+1,taillen*sizeof(raxNode**)+valuelen);
  
      /* 4. Update size. */
      parent->size--;
  
      /* realloc the node according to the theoretical memory usage, to free
       * data if we are over-allocating right now. */
      raxNode *newnode = rax_realloc(parent,raxNodeCurrentLength(parent));
      if (newnode) {
          debugnode("raxRemoveChild after", newnode);
      }
      /* Note: if rax_realloc() fails we just return the old address, which
       * is valid. */
      return newnode ? newnode : parent;
  }
  
  /* Remove the specified item. Returns 1 if the item was found and
   * deleted, 0 otherwise. */
  int raxRemove(rax *rax, unsigned char *s, size_t len, void **old) {
      raxNode *h;
      raxStack ts;
  
      debugf("### Delete: %.*s\n", (int)len, s);
      raxStackInit(&ts);
      int splitpos = 0;
      size_t i = raxLowWalk(rax,s,len,&h,NULL,&splitpos,&ts);
      if (i != len || (h->iscompr && splitpos != 0) || !h->iskey) {
          raxStackFree(&ts);
          return 0;
      }
      if (old) *old = raxGetData(h);
      h->iskey = 0;
      rax->numele--;
  
      /* If this node has no children, the deletion needs to reclaim the
       * no longer used nodes. This is an iterative process that needs to
       * walk the three upward, deleting all the nodes with just one child
       * that are not keys, until the head of the rax is reached or the first
       * node with more than one child is found. */
  
      int trycompress = 0; /* Will be set to 1 if we should try to optimize the
                              tree resulting from the deletion. */
  
      if (h->size == 0) {
          debugf("Key deleted in node without children. Cleanup needed.\n");
          raxNode *child = NULL;
          while(h != rax->head) {
              child = h;
              debugf("Freeing child %p [%.*s] key:%d\n", (void*)child,
                  (int)child->size, (char*)child->data, child->iskey);
              rax_free(child);
              rax->numnodes--;
              h = raxStackPop(&ts);
               /* If this node has more then one child, or actually holds
                * a key, stop here. */
              if (h->iskey || (!h->iscompr && h->size != 1)) break;
          }
          if (child) {
              debugf("Unlinking child %p from parent %p\n",
                  (void*)child, (void*)h);
              raxNode *new = raxRemoveChild(h,child);
              if (new != h) {
                  raxNode *parent = raxStackPeek(&ts);
                  raxNode **parentlink;
                  if (parent == NULL) {
                      parentlink = &rax->head;
                  } else {
                      parentlink = raxFindParentLink(parent,h);
                  }
                  memcpy(parentlink,&new,sizeof(new));
              }
  
              /* If after the removal the node has just a single child
               * and is not a key, we need to try to compress it. */
              if (new->size == 1 && new->iskey == 0) {
                  trycompress = 1;
                  h = new;
              }
          }
      } else if (h->size == 1) {
          /* If the node had just one child, after the removal of the key
           * further compression with adjacent nodes is potentially possible. */
          trycompress = 1;
      }
  
      /* Don't try node compression if our nodes pointers stack is not
       * complete because of OOM while executing raxLowWalk() */
      if (trycompress && ts.oom) trycompress = 0;
  
      /* Recompression: if trycompress is true, 'h' points to a radix tree node
       * that changed in a way that could allow to compress nodes in this
       * sub-branch. Compressed nodes represent chains of nodes that are not
       * keys and have a single child, so there are two deletion events that
       * may alter the tree so that further compression is needed:
       *
       * 1) A node with a single child was a key and now no longer is a key.
       * 2) A node with two children now has just one child.
       *
       * We try to navigate upward till there are other nodes that can be
       * compressed, when we reach the upper node which is not a key and has
       * a single child, we scan the chain of children to collect the
       * compressible part of the tree, and replace the current node with the
       * new one, fixing the child pointer to reference the first non
       * compressible node.
       *
       * Example of case "1". A tree stores the keys "FOO" = 1 and
       * "FOOBAR" = 2:
       *
       *
       * "FOO" -> "BAR" -> [] (2)
       *           (1)
       *
       * After the removal of "FOO" the tree can be compressed as:
       *
       * "FOOBAR" -> [] (2)
       *
       *
       * Example of case "2". A tree stores the keys "FOOBAR" = 1 and
       * "FOOTER" = 2:
       *
       *          |B| -> "AR" -> [] (1)
       * "FOO" -> |-|
       *          |T| -> "ER" -> [] (2)
       *
       * After the removal of "FOOTER" the resulting tree is:
       *
       * "FOO" -> |B| -> "AR" -> [] (1)
       *
       * That can be compressed into:
       *
       * "FOOBAR" -> [] (1)
       */
      if (trycompress) {
          debugf("After removing %.*s:\n", (int)len, s);
          debugnode("Compression may be needed",h);
          debugf("Seek start node\n");
  
          /* Try to reach the upper node that is compressible.
           * At the end of the loop 'h' will point to the first node we
           * can try to compress and 'parent' to its parent. */
          raxNode *parent;
          while(1) {
              parent = raxStackPop(&ts);
              if (!parent || parent->iskey ||
                  (!parent->iscompr && parent->size != 1)) break;
              h = parent;
              debugnode("Going up to",h);
          }
          raxNode *start = h; /* Compression starting node. */
  
          /* Scan chain of nodes we can compress. */
          size_t comprsize = h->size;
          int nodes = 1;
          while(h->size != 0) {
              raxNode **cp = raxNodeLastChildPtr(h);
              memcpy(&h,cp,sizeof(h));
              if (h->iskey || (!h->iscompr && h->size != 1)) break;
              /* Stop here if going to the next node would result into
               * a compressed node larger than h->size can hold. */
              if (comprsize + h->size > RAX_NODE_MAX_SIZE) break;
              nodes++;
              comprsize += h->size;
          }
          if (nodes > 1) {
              /* If we can compress, create the new node and populate it. */
              size_t nodesize =
                  sizeof(raxNode)+comprsize+raxPadding(comprsize)+sizeof(raxNode*);
              raxNode *new = rax_malloc(nodesize);
              /* An out of memory here just means we cannot optimize this
               * node, but the tree is left in a consistent state. */
              if (new == NULL) {
                  raxStackFree(&ts);
                  return 1;
              }
              new->iskey = 0;
              new->isnull = 0;
              new->iscompr = 1;
              new->size = comprsize;
              rax->numnodes++;
  
              /* Scan again, this time to populate the new node content and
               * to fix the new node child pointer. At the same time we free
               * all the nodes that we'll no longer use. */
              comprsize = 0;
              h = start;
              while(h->size != 0) {
                  memcpy(new->data+comprsize,h->data,h->size);
                  comprsize += h->size;
                  raxNode **cp = raxNodeLastChildPtr(h);
                  raxNode *tofree = h;
                  memcpy(&h,cp,sizeof(h));
                  rax_free(tofree); rax->numnodes--;
                  if (h->iskey || (!h->iscompr && h->size != 1)) break;
              }
              debugnode("New node",new);
  
              /* Now 'h' points to the first node that we still need to use,
               * so our new node child pointer will point to it. */
              raxNode **cp = raxNodeLastChildPtr(new);
              memcpy(cp,&h,sizeof(h));
  
              /* Fix parent link. */
              if (parent) {
                  raxNode **parentlink = raxFindParentLink(parent,start);
                  memcpy(parentlink,&new,sizeof(new));
              } else {
                  rax->head = new;
              }
  
              debugf("Compressed %d nodes, %d total bytes\n",
                  nodes, (int)comprsize);
          }
      }
      raxStackFree(&ts);
      return 1;
  }
  
  /* This is the core of raxFree(): performs a depth-first scan of the
   * tree and releases all the nodes found. */
  void raxRecursiveFree(rax *rax, raxNode *n, void (*free_callback)(void*)) {
      debugnode("free traversing",n);
      int numchildren = n->iscompr ? 1 : n->size;
      raxNode **cp = raxNodeLastChildPtr(n);
      while(numchildren--) {
          raxNode *child;
          memcpy(&child,cp,sizeof(child));
          raxRecursiveFree(rax,child,free_callback);
          cp--;
      }
      debugnode("free depth-first",n);
      if (free_callback && n->iskey && !n->isnull)
          free_callback(raxGetData(n));
      rax_free(n);
      rax->numnodes--;
  }
  
  /* Free a whole radix tree, calling the specified callback in order to
   * free the auxiliary data. */
  void raxFreeWithCallback(rax *rax, void (*free_callback)(void*)) {
      raxRecursiveFree(rax,rax->head,free_callback);
      assert(rax->numnodes == 0);
      rax_free(rax);
  }
  
  /* Free a whole radix tree. */
  void raxFree(rax *rax) {
      raxFreeWithCallback(rax,NULL);
  }
  
  /* ------------------------------- Iterator --------------------------------- */
  
  /* Initialize a Rax iterator. This call should be performed a single time
   * to initialize the iterator, and must be followed by a raxSeek() call,
   * otherwise the raxPrev()/raxNext() functions will just return EOF. */
  void raxStart(raxIterator *it, rax *rt) {
      it->flags = RAX_ITER_EOF; /* No crash if the iterator is not seeked. */
      it->rt = rt;
      it->key_len = 0;
      it->key = it->key_static_string;
      it->key_max = RAX_ITER_STATIC_LEN;
      it->data = NULL;
      it->node_cb = NULL;
      raxStackInit(&it->stack);
  }
  
  /* Append characters at the current key string of the iterator 'it'. This
   * is a low level function used to implement the iterator, not callable by
   * the user. Returns 0 on out of memory, otherwise 1 is returned. */
  int raxIteratorAddChars(raxIterator *it, unsigned char *s, size_t len) {
      if (it->key_max < it->key_len+len) {
          unsigned char *old = (it->key == it->key_static_string) ? NULL :
                                                                    it->key;
          size_t new_max = (it->key_len+len)*2;
          it->key = rax_realloc(old,new_max);
          if (it->key == NULL) {
              it->key = (!old) ? it->key_static_string : old;
              errno = ENOMEM;
              return 0;
          }
          if (old == NULL) memcpy(it->key,it->key_static_string,it->key_len);
          it->key_max = new_max;
      }
      /* Use memmove since there could be an overlap between 's' and
       * it->key when we use the current key in order to re-seek. */
      memmove(it->key+it->key_len,s,len);
      it->key_len += len;
      return 1;
  }
  
  /* Remove the specified number of chars from the right of the current
   * iterator key. */
  void raxIteratorDelChars(raxIterator *it, size_t count) {
      it->key_len -= count;
  }
  
  /* Do an iteration step towards the next element. At the end of the step the
   * iterator key will represent the (new) current key. If it is not possible
   * to step in the specified direction since there are no longer elements, the
   * iterator is flagged with RAX_ITER_EOF.
   *
   * If 'noup' is true the function starts directly scanning for the next
   * lexicographically smaller children, and the current node is already assumed
   * to be the parent of the last key node, so the first operation to go back to
   * the parent will be skipped. This option is used by raxSeek() when
   * implementing seeking a non existing element with the ">" or "<" options:
   * the starting node is not a key in that particular case, so we start the scan
   * from a node that does not represent the key set.
   *
   * The function returns 1 on success or 0 on out of memory. */
  int raxIteratorNextStep(raxIterator *it, int noup) {
      if (it->flags & RAX_ITER_EOF) {
          return 1;
      } else if (it->flags & RAX_ITER_JUST_SEEKED) {
          it->flags &= ~RAX_ITER_JUST_SEEKED;
          return 1;
      }
  
      /* Save key len, stack items and the node where we are currently
       * so that on iterator EOF we can restore the current key and state. */
      size_t orig_key_len = it->key_len;
      size_t orig_stack_items = it->stack.items;
      raxNode *orig_node = it->node;
  
      while(1) {
          int children = it->node->iscompr ? 1 : it->node->size;
          if (!noup && children) {
              debugf("GO DEEPER\n");
              /* Seek the lexicographically smaller key in this subtree, which
               * is the first one found always going towards the first child
               * of every successive node. */
              if (!raxStackPush(&it->stack,it->node)) return 0;
              raxNode **cp = raxNodeFirstChildPtr(it->node);
              if (!raxIteratorAddChars(it,it->node->data,
                  it->node->iscompr ? it->node->size : 1)) return 0;
              memcpy(&it->node,cp,sizeof(it->node));
              /* Call the node callback if any, and replace the node pointer
               * if the callback returns true. */
              if (it->node_cb && it->node_cb(&it->node))
                  memcpy(cp,&it->node,sizeof(it->node));
              /* For "next" step, stop every time we find a key along the
               * way, since the key is lexicographically smaller compared to
               * what follows in the sub-children. */
              if (it->node->iskey) {
                  it->data = raxGetData(it->node);
                  return 1;
              }
          } else {
              /* If we finished exploring the previous sub-tree, switch to the
               * new one: go upper until a node is found where there are
               * children representing keys lexicographically greater than the
               * current key. */
              while(1) {
                  int old_noup = noup;
  
                  /* Already on head? Can't go up, iteration finished. */
                  if (!noup && it->node == it->rt->head) {
                      it->flags |= RAX_ITER_EOF;
                      it->stack.items = orig_stack_items;
                      it->key_len = orig_key_len;
                      it->node = orig_node;
                      return 1;
                  }
                  /* If there are no children at the current node, try parent's
                   * next child. */
                  unsigned char prevchild = it->key[it->key_len-1];
                  if (!noup) {
                      it->node = raxStackPop(&it->stack);
                  } else {
                      noup = 0;
                  }
                  /* Adjust the current key to represent the node we are
                   * at. */
                  int todel = it->node->iscompr ? it->node->size : 1;
                  raxIteratorDelChars(it,todel);
  
                  /* Try visiting the next child if there was at least one
                   * additional child. */
                  if (!it->node->iscompr && it->node->size > (old_noup ? 0 : 1)) {
                      raxNode **cp = raxNodeFirstChildPtr(it->node);
                      int i = 0;
                      while (i < it->node->size) {
                          debugf("SCAN NEXT %c\n", it->node->data[i]);
                          if (it->node->data[i] > prevchild) break;
                          i++;
                          cp++;
                      }
                      if (i != it->node->size) {
                          debugf("SCAN found a new node\n");
                          raxIteratorAddChars(it,it->node->data+i,1);
                          if (!raxStackPush(&it->stack,it->node)) return 0;
                          memcpy(&it->node,cp,sizeof(it->node));
                          /* Call the node callback if any, and replace the node
                           * pointer if the callback returns true. */
                          if (it->node_cb && it->node_cb(&it->node))
                              memcpy(cp,&it->node,sizeof(it->node));
                          if (it->node->iskey) {
                              it->data = raxGetData(it->node);
                              return 1;
                          }
                          break;
                      }
                  }
              }
          }
      }
  }
  
  /* Seek the greatest key in the subtree at the current node. Return 0 on
   * out of memory, otherwise 1. This is a helper function for different
   * iteration functions below. */
  int raxSeekGreatest(raxIterator *it) {
      while(it->node->size) {
          if (it->node->iscompr) {
              if (!raxIteratorAddChars(it,it->node->data,
                  it->node->size)) return 0;
          } else {
              if (!raxIteratorAddChars(it,it->node->data+it->node->size-1,1))
                  return 0;
          }
          raxNode **cp = raxNodeLastChildPtr(it->node);
          if (!raxStackPush(&it->stack,it->node)) return 0;
          memcpy(&it->node,cp,sizeof(it->node));
      }
      return 1;
  }
  
  /* Like raxIteratorNextStep() but implements an iteration step moving
   * to the lexicographically previous element. The 'noup' option has a similar
   * effect to the one of raxIteratorNextStep(). */
  int raxIteratorPrevStep(raxIterator *it, int noup) {
      if (it->flags & RAX_ITER_EOF) {
          return 1;
      } else if (it->flags & RAX_ITER_JUST_SEEKED) {
          it->flags &= ~RAX_ITER_JUST_SEEKED;
          return 1;
      }
  
      /* Save key len, stack items and the node where we are currently
       * so that on iterator EOF we can restore the current key and state. */
      size_t orig_key_len = it->key_len;
      size_t orig_stack_items = it->stack.items;
      raxNode *orig_node = it->node;
  
      while(1) {
          int old_noup = noup;
  
          /* Already on head? Can't go up, iteration finished. */
          if (!noup && it->node == it->rt->head) {
              it->flags |= RAX_ITER_EOF;
              it->stack.items = orig_stack_items;
              it->key_len = orig_key_len;
              it->node = orig_node;
              return 1;
          }
  
          unsigned char prevchild = it->key[it->key_len-1];
          if (!noup) {
              it->node = raxStackPop(&it->stack);
          } else {
              noup = 0;
          }
  
          /* Adjust the current key to represent the node we are
           * at. */
          int todel = it->node->iscompr ? it->node->size : 1;
          raxIteratorDelChars(it,todel);
  
          /* Try visiting the prev child if there is at least one
           * child. */
          if (!it->node->iscompr && it->node->size > (old_noup ? 0 : 1)) {
              raxNode **cp = raxNodeLastChildPtr(it->node);
              int i = it->node->size-1;
              while (i >= 0) {
                  debugf("SCAN PREV %c\n", it->node->data[i]);
                  if (it->node->data[i] < prevchild) break;
                  i--;
                  cp--;
              }
              /* If we found a new subtree to explore in this node,
               * go deeper following all the last children in order to
               * find the key lexicographically greater. */
              if (i != -1) {
                  debugf("SCAN found a new node\n");
                  /* Enter the node we just found. */
                  if (!raxIteratorAddChars(it,it->node->data+i,1)) return 0;
                  if (!raxStackPush(&it->stack,it->node)) return 0;
                  memcpy(&it->node,cp,sizeof(it->node));
                  /* Seek sub-tree max. */
                  if (!raxSeekGreatest(it)) return 0;
              }
          }
  
          /* Return the key: this could be the key we found scanning a new
           * subtree, or if we did not find a new subtree to explore here,
           * before giving up with this node, check if it's a key itself. */
          if (it->node->iskey) {
              it->data = raxGetData(it->node);
              return 1;
          }
      }
  }
  
  /* Seek an iterator at the specified element.
   * Return 0 if the seek failed for syntax error or out of memory. Otherwise
   * 1 is returned. When 0 is returned for out of memory, errno is set to
   * the ENOMEM value. */
  int raxSeek(raxIterator *it, const char *op, unsigned char *ele, size_t len) {
      int eq = 0, lt = 0, gt = 0, first = 0, last = 0;
  
      it->stack.items = 0; /* Just resetting. Initialized by raxStart(). */
      it->flags |= RAX_ITER_JUST_SEEKED;
      it->flags &= ~RAX_ITER_EOF;
      it->key_len = 0;
      it->node = NULL;
  
      /* Set flags according to the operator used to perform the seek. */
      if (op[0] == '>') {
          gt = 1;
          if (op[1] == '=') eq = 1;
      } else if (op[0] == '<') {
          lt = 1;
          if (op[1] == '=') eq = 1;
      } else if (op[0] == '=') {
          eq = 1;
      } else if (op[0] == '^') {
          first = 1;
      } else if (op[0] == '$') {
          last = 1;
      } else {
          errno = 0;
          return 0; /* Error. */
      }
  
      /* If there are no elements, set the EOF condition immediately and
       * return. */
      if (it->rt->numele == 0) {
          it->flags |= RAX_ITER_EOF;
          return 1;
      }
  
      if (first) {
          /* Seeking the first key greater or equal to the empty string
           * is equivalent to seeking the smaller key available. */
          return raxSeek(it,">=",NULL,0);
      }
  
      if (last) {
          /* Find the greatest key taking always the last child till a
           * final node is found. */
          it->node = it->rt->head;
          if (!raxSeekGreatest(it)) return 0;
          assert(it->node->iskey);
          it->data = raxGetData(it->node);
          return 1;
      }
  
      /* We need to seek the specified key. What we do here is to actually
       * perform a lookup, and later invoke the prev/next key code that
       * we already use for iteration. */
      int splitpos = 0;
      size_t i = raxLowWalk(it->rt,ele,len,&it->node,NULL,&splitpos,&it->stack);
  
      /* Return OOM on incomplete stack info. */
      if (it->stack.oom) return 0;
  
      if (eq && i == len && (!it->node->iscompr || splitpos == 0) &&
          it->node->iskey)
      {
          /* We found our node, since the key matches and we have an
           * "equal" condition. */
          if (!raxIteratorAddChars(it,ele,len)) return 0; /* OOM. */
          it->data = raxGetData(it->node);
      } else if (lt || gt) {
          /* Exact key not found or eq flag not set. We have to set as current
           * key the one represented by the node we stopped at, and perform
           * a next/prev operation to seek. To reconstruct the key at this node
           * we start from the parent and go to the current node, accumulating
           * the characters found along the way. */
          if (!raxStackPush(&it->stack,it->node)) return 0;
          for (size_t j = 1; j < it->stack.items; j++) {
              raxNode *parent = it->stack.stack[j-1];
              raxNode *child = it->stack.stack[j];
              if (parent->iscompr) {
                  if (!raxIteratorAddChars(it,parent->data,parent->size))
                      return 0;
              } else {
                  raxNode **cp = raxNodeFirstChildPtr(parent);
                  unsigned char *p = parent->data;
                  while(1) {
                      raxNode *aux;
                      memcpy(&aux,cp,sizeof(aux));
                      if (aux == child) break;
                      cp++;
                      p++;
                  }
                  if (!raxIteratorAddChars(it,p,1)) return 0;
              }
          }
          raxStackPop(&it->stack);
  
          /* We need to set the iterator in the correct state to call next/prev
           * step in order to seek the desired element. */
          debugf("After initial seek: i=%d len=%d key=%.*s\n",
              (int)i, (int)len, (int)it->key_len, it->key);
          if (i != len && !it->node->iscompr) {
              /* If we stopped in the middle of a normal node because of a
               * mismatch, add the mismatching character to the current key
               * and call the iterator with the 'noup' flag so that it will try
               * to seek the next/prev child in the current node directly based
               * on the mismatching character. */
              if (!raxIteratorAddChars(it,ele+i,1)) return 0;
              debugf("Seek normal node on mismatch: %.*s\n",
                  (int)it->key_len, (char*)it->key);
  
              it->flags &= ~RAX_ITER_JUST_SEEKED;
              if (lt && !raxIteratorPrevStep(it,1)) return 0;
              if (gt && !raxIteratorNextStep(it,1)) return 0;
              it->flags |= RAX_ITER_JUST_SEEKED; /* Ignore next call. */
          } else if (i != len && it->node->iscompr) {
              debugf("Compressed mismatch: %.*s\n",
                  (int)it->key_len, (char*)it->key);
              /* In case of a mismatch within a compressed node. */
              int nodechar = it->node->data[splitpos];
              int keychar = ele[i];
              it->flags &= ~RAX_ITER_JUST_SEEKED;
              if (gt) {
                  /* If the key the compressed node represents is greater
                   * than our seek element, continue forward, otherwise set the
                   * state in order to go back to the next sub-tree. */
                  if (nodechar > keychar) {
                      if (!raxIteratorNextStep(it,0)) return 0;
                  } else {
                      if (!raxIteratorAddChars(it,it->node->data,it->node->size))
                          return 0;
                      if (!raxIteratorNextStep(it,1)) return 0;
                  }
              }
              if (lt) {
                  /* If the key the compressed node represents is smaller
                   * than our seek element, seek the greater key in this
                   * subtree, otherwise set the state in order to go back to
                   * the previous sub-tree. */
                  if (nodechar < keychar) {
                      if (!raxSeekGreatest(it)) return 0;
                      it->data = raxGetData(it->node);
                  } else {
                      if (!raxIteratorAddChars(it,it->node->data,it->node->size))
                          return 0;
                      if (!raxIteratorPrevStep(it,1)) return 0;
                  }
              }
              it->flags |= RAX_ITER_JUST_SEEKED; /* Ignore next call. */
          } else {
              debugf("No mismatch: %.*s\n",
                  (int)it->key_len, (char*)it->key);
              /* If there was no mismatch we are into a node representing the
               * key, (but which is not a key or the seek operator does not
               * include 'eq'), or we stopped in the middle of a compressed node
               * after processing all the key. Continue iterating as this was
               * a legitimate key we stopped at. */
              it->flags &= ~RAX_ITER_JUST_SEEKED;
              if (it->node->iscompr && it->node->iskey && splitpos && lt) {
                  /* If we stopped in the middle of a compressed node with
                   * perfect match, and the condition is to seek a key "<" than
                   * the specified one, then if this node is a key it already
                   * represents our match. For instance we may have nodes:
                   *
                   * "f" -> "oobar" = 1 -> "" = 2
                   *
                   * Representing keys "f" = 1, "foobar" = 2. A seek for
                   * the key < "foo" will stop in the middle of the "oobar"
                   * node, but will be our match, representing the key "f".
                   *
                   * So in that case, we don't seek backward. */
                  it->data = raxGetData(it->node);
              } else {
                  if (gt && !raxIteratorNextStep(it,0)) return 0;
                  if (lt && !raxIteratorPrevStep(it,0)) return 0;
              }
              it->flags |= RAX_ITER_JUST_SEEKED; /* Ignore next call. */
          }
      } else {
          /* If we are here just eq was set but no match was found. */
          it->flags |= RAX_ITER_EOF;
          return 1;
      }
      return 1;
  }
  
  /* Go to the next element in the scope of the iterator 'it'.
   * If EOF (or out of memory) is reached, 0 is returned, otherwise 1 is
   * returned. In case 0 is returned because of OOM, errno is set to ENOMEM. */
  int raxNext(raxIterator *it) {
      if (!raxIteratorNextStep(it,0)) {
          errno = ENOMEM;
          return 0;
      }
      if (it->flags & RAX_ITER_EOF) {
          errno = 0;
          return 0;
      }
      return 1;
  }
  
  /* Go to the previous element in the scope of the iterator 'it'.
   * If EOF (or out of memory) is reached, 0 is returned, otherwise 1 is
   * returned. In case 0 is returned because of OOM, errno is set to ENOMEM. */
  int raxPrev(raxIterator *it) {
      if (!raxIteratorPrevStep(it,0)) {
          errno = ENOMEM;
          return 0;
      }
      if (it->flags & RAX_ITER_EOF) {
          errno = 0;
          return 0;
      }
      return 1;
  }
  
  /* Perform a random walk starting in the current position of the iterator.
   * Return 0 if the tree is empty or on out of memory. Otherwise 1 is returned
   * and the iterator is set to the node reached after doing a random walk
   * of 'steps' steps. If the 'steps' argument is 0, the random walk is performed
   * using a random number of steps between 1 and two times the logarithm of
   * the number of elements.
   *
   * NOTE: if you use this function to generate random elements from the radix
   * tree, expect a disappointing distribution. A random walk produces good
   * random elements if the tree is not sparse, however in the case of a radix
   * tree certain keys will be reported much more often than others. At least
   * this function should be able to explore every possible element eventually. */
  int raxRandomWalk(raxIterator *it, size_t steps) {
      if (it->rt->numele == 0) {
          it->flags |= RAX_ITER_EOF;
          return 0;
      }
  
      if (steps == 0) {
          size_t fle = 1+floor(log(it->rt->numele));
          fle *= 2;
          steps = 1 + rand() % fle;
      }
  
      raxNode *n = it->node;
      while(steps > 0 || !n->iskey) {
          int numchildren = n->iscompr ? 1 : n->size;
          int r = rand() % (numchildren+(n != it->rt->head));
  
          if (r == numchildren) {
              /* Go up to parent. */
              n = raxStackPop(&it->stack);
              int todel = n->iscompr ? n->size : 1;
              raxIteratorDelChars(it,todel);
          } else {
              /* Select a random child. */
              if (n->iscompr) {
                  if (!raxIteratorAddChars(it,n->data,n->size)) return 0;
              } else {
                  if (!raxIteratorAddChars(it,n->data+r,1)) return 0;
              }
              raxNode **cp = raxNodeFirstChildPtr(n)+r;
              if (!raxStackPush(&it->stack,n)) return 0;
              memcpy(&n,cp,sizeof(n));
          }
          if (n->iskey) steps--;
      }
      it->node = n;
      it->data = raxGetData(it->node);
      return 1;
  }
  
  /* Compare the key currently pointed by the iterator to the specified
   * key according to the specified operator. Returns 1 if the comparison is
   * true, otherwise 0 is returned. */
  int raxCompare(raxIterator *iter, const char *op, unsigned char *key, size_t key_len) {
      int eq = 0, lt = 0, gt = 0;
  
      if (op[0] == '=' || op[1] == '=') eq = 1;
      if (op[0] == '>') gt = 1;
      else if (op[0] == '<') lt = 1;
      else if (op[1] != '=') return 0; /* Syntax error. */
  
      size_t minlen = key_len < iter->key_len ? key_len : iter->key_len;
      int cmp = memcmp(iter->key,key,minlen);
  
      /* Handle == */
      if (lt == 0 && gt == 0) return cmp == 0 && key_len == iter->key_len;
  
      /* Handle >, >=, <, <= */
      if (cmp == 0) {
          /* Same prefix: longer wins. */
          if (eq && key_len == iter->key_len) return 1;
          else if (lt) return iter->key_len < key_len;
          else if (gt) return iter->key_len > key_len;
          else return 0; /* Avoid warning, just 'eq' is handled before. */
      } else if (cmp > 0) {
          return gt ? 1 : 0;
      } else /* (cmp < 0) */ {
          return lt ? 1 : 0;
      }
  }
  
  /* Free the iterator. */
  void raxStop(raxIterator *it) {
      if (it->key != it->key_static_string) rax_free(it->key);
      raxStackFree(&it->stack);
  }
  
  /* Return if the iterator is in an EOF state. This happens when raxSeek()
   * failed to seek an appropriate element, so that raxNext() or raxPrev()
   * will return zero, or when an EOF condition was reached while iterating
   * with raxNext() and raxPrev(). */
  int raxEOF(raxIterator *it) {
      return it->flags & RAX_ITER_EOF;
  }
  
  /* Return the number of elements inside the radix tree. */
  uint64_t raxSize(rax *rax) {
      return rax->numele;
  }
  
  /* ----------------------------- Introspection ------------------------------ */
  
  /* This function is mostly used for debugging and learning purposes.
   * It shows an ASCII representation of a tree on standard output, outline
   * all the nodes and the contained keys.
   *
   * The representation is as follow:
   *
   *  "foobar" (compressed node)
   *  [abc] (normal node with three children)
   *  [abc]=0x12345678 (node is a key, pointing to value 0x12345678)
   *  [] (a normal empty node)
   *
   *  Children are represented in new indented lines, each children prefixed by
   *  the "`-(x)" string, where "x" is the edge byte.
   *
   *  [abc]
   *   `-(a) "ladin"
   *   `-(b) [kj]
   *   `-(c) []
   *
   *  However when a node has a single child the following representation
   *  is used instead:
   *
   *  [abc] -> "ladin" -> []
   */
  
  /* The actual implementation of raxShow(). */
  void raxRecursiveShow(int level, int lpad, raxNode *n) {
      char s = n->iscompr ? '"' : '[';
      char e = n->iscompr ? '"' : ']';
  
      int numchars = printf("%c%.*s%c", s, n->size, n->data, e);
      if (n->iskey) {
          numchars += printf("=%p",raxGetData(n));
      }
  
      int numchildren = n->iscompr ? 1 : n->size;
      /* Note that 7 and 4 magic constants are the string length
       * of " `-(x) " and " -> " respectively. */
      if (level) {
          lpad += (numchildren > 1) ? 7 : 4;
          if (numchildren == 1) lpad += numchars;
      }
      raxNode **cp = raxNodeFirstChildPtr(n);
      for (int i = 0; i < numchildren; i++) {
          char *branch = " `-(%c) ";
          if (numchildren > 1) {
              printf("\n");
              for (int j = 0; j < lpad; j++) putchar(' ');
              printf(branch,n->data[i]);
          } else {
              printf(" -> ");
          }
          raxNode *child;
          memcpy(&child,cp,sizeof(child));
          raxRecursiveShow(level+1,lpad,child);
          cp++;
      }
  }
  
  /* Show a tree, as outlined in the comment above. */
  void raxShow(rax *rax) {
      raxRecursiveShow(0,0,rax->head);
      putchar('\n');
  }
  
  /* Used by debugnode() macro to show info about a given node. */
  void raxDebugShowNode(const char *msg, raxNode *n) {
      if (raxDebugMsg == 0) return;
      printf("%s: %p [%.*s] key:%u size:%u children:",
          msg, (void*)n, (int)n->size, (char*)n->data, n->iskey, n->size);
      int numcld = n->iscompr ? 1 : n->size;
      raxNode **cldptr = raxNodeLastChildPtr(n) - (numcld-1);
      while(numcld--) {
          raxNode *child;
          memcpy(&child,cldptr,sizeof(child));
          cldptr++;
          printf("%p ", (void*)child);
      }
      printf("\n");
      fflush(stdout);
  }
  
  /* Touch all the nodes of a tree returning a check sum. This is useful
   * in order to make Valgrind detect if there is something wrong while
   * reading the data structure.
   *
   * This function was used in order to identify Rax bugs after a big refactoring
   * using this technique:
   *
   * 1. The rax-test is executed using Valgrind, adding a printf() so that for
   *    the fuzz tester we see what iteration in the loop we are in.
   * 2. After every modification of the radix tree made by the fuzz tester
   *    in rax-test.c, we add a call to raxTouch().
   * 3. Now as soon as an operation will corrupt the tree, raxTouch() will
   *    detect it (via Valgrind) immediately. We can add more calls to narrow
   *    the state.
   * 4. At this point a good idea is to enable Rax debugging messages immediately
   *    before the moment the tree is corrupted, to see what happens.
   */
  unsigned long raxTouch(raxNode *n) {
      debugf("Touching %p\n", (void*)n);
      unsigned long sum = 0;
      if (n->iskey) {
          sum += (unsigned long)raxGetData(n);
      }
  
      int numchildren = n->iscompr ? 1 : n->size;
      raxNode **cp = raxNodeFirstChildPtr(n);
      int count = 0;
      for (int i = 0; i < numchildren; i++) {
          if (numchildren > 1) {
              sum += (long)n->data[i];
          }
          raxNode *child;
          memcpy(&child,cp,sizeof(child));
          if (child == (void*)0x65d1760) count++;
          if (count > 1) exit(1);
          sum += raxTouch(child);
          cp++;
      }
      return sum;
  }
  